Observability of probabilistic Boolean multiplex networks

Abstract

This study focuses on the observability of the probabilistic Boolean multiplex network. Firstly, the dynamical model and structure of probabilistic Boolean multiplex network are proposed. Using the semi‐tensor product method, the logical dynamics of probabilistic Boolean multiplex network is converted into an equivalent algebraic representation. Then, the condition for the observability of probabilistic Boolean multiplex network is obtained. Finally, the proposed result is effectively illustrated by a numerical example.

Further results for synchronization of two coupled Boolean networks

“…, then, an algebraic form for (8a) and (8b) is obtained, v(t + 1) = Fv(t), w(t + 1) = Gv(t)w(t), where F = 𝛿 8 [4,7,5,8,3,6,4,7], G = 𝛿 8 [3,3,3,3,3,4,3,4, … ] ∈  8×64 , the detailed information for matrix G is omitted here. Let 𝜉(t) = v(t)w(t) ∈ Δ 64 , then we get…”

“…Then, an algebraic form for (10a) and (10b) is obtained, v(t + 1) = Fv(t), w(t + 1) = Gv(t)w(t), where F = 𝛿 8 [3,7,8,8,1,5,6,6], G = 𝛿 8 [5, 1, 6, 2, 7, 3, 8, 4, … ] ∈  8×64 , the detailed information for matrix G is omitted here. Then, we get 64 and 𝛿 62 64 of (11) before and after {1, 2}-perturbation 𝜉(t + 1) = L𝜉(t), (11) where L = 𝛿 64 [21, 17, 22, 18, 23, 19, 24, 20,…”

“…To overcome this difficulty, Cheng et al derived the equivalent algebraic form of BNs by using the semi-tensor product (STP) of matrices in 2010 [4]. Then, the researches on BNs are further developed, includ-ing controllability, observability, optimal control, synchronization, output tracking, and state estimation [5][6][7][8][9][10][11][12][13][14][15][16].…”

On a Class of Tensor Markov Fields

“…After having considered some of the properties of this class of Tensor Markov Fields, it may become evident that aside from purely theoretical importance, there is a number of important applications that may arise as probabilistic graphical models in tensor valued problems, among the ones that are somewhat evident are the following: The analysis of multidimensional biomolecular networks such as the ones arising from multi-omic experiments (For a real-life example, see Figure 4 ) [ 8 , 9 , 10 ]; Probabilistic graphical models in computer vision (especially 3D reconstructions and 4D [3D+time] rendering) [ 11 ]; The study of fracture mechanics in continuous deformable media [ 12 ]; Probabilistic network models for seismic dynamics [ 13 ]; Boolean networks in control theory [ 14 ]. …”

Set reachability and set stability of Boolean networks with state‐dependent asynchronous updating rule

“…Recently, semi-tensor product (STP) of matrices has emerged as a powerful tool to express and analyze Boolean control networks, facilitating the equivalent algebraic representation of a logical expression [20,25]. Based on the algebraic form, two basic methods, zeroing [23] and eliminating [21] undesirable states and controls, were proposed to study Boolean control networks with state and input constraints.…”